A milling operation using automatic machines requires immediate stopping of said machines as soon as the required depth of milling is achieved relative to the surface of the piece to be machined. This depth must be very exactly observed so that, during mounting of the rivets and the securement of the latter in holes and milled recesses of the machined piece, no rivet will extend above or below the surface of the piece, which would give rise to undesirable aerodynamic turbulence over the assembly of the pieces.